Question: Find the domain of the real-valued function $$f(x)=\sqrt{-10x^2-11x+6}.$$ Give the endpoints in your answer as common fractions, not mixed numbers or decimals.
We need $-10x^2-11x+6\geq 0$.  The quadratic factors as $$(2x+3)(-5x+2) \ge 0.$$ Thus the zeroes of the quadratic are at $-\frac{3}{2}$ and $\frac{2}{5}$.  Since the quadratic opens downward, it is nonnegative between the zeroes.  So the domain is $x \in \boxed{\left[-\frac{3}{2}, \frac{2}{5}\right]}$.